Partially complex modulated filter bank

ABSTRACT

An apparatus for processing a plurality of real-valued subband signals using a first real-valued subband signal and a second real-valued subband signal to provide at least a complex-valued subband signal comprises a multiband filter for providing an intermediate real-valued subband signal and a calculator for providing the complex-valued subband signal by combining a real-valued subband signal from the plurality of real-valued subband signals and the intermediate subband signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This Application is a divisional of U.S. patent application Ser. No.11/463,263, entitled Partially Complex Modulated Filter Bank, filed 8Aug. 2006 now U.S. Pat. No. 7,917,561 which claims priority to U.S.Provisional Application No. 60/733,682, entitled Partially ComplexModulated Filter Bank, filed 3 Nov. 2005, and also claims priority toSwedish Patent Application No. 0502049-0, filed 16 Sep. 2005, all ofwhich are incorporated herein in its entirety by this reference thereto.

FIELD OF THE INVENTION

The present invention relates to an apparatus and method for processinga plurality of complex-valued subband signals and an apparatus andmethod for processing a plurality of real-valued subband signals,especially in the field of encoding and decoding of audio signals.

BACKGROUND OF THE INVENTION AND PRIOR ART

It has been shown in [P. Ekstrand, “Bandwidth extension of audio signalsby spectral band replication”, Proc. 1^(st) IEEE Benelux Workshop onModel based Processing and Coding of Audio (MPCA-2002), pp. 53-58,Leuven, Belgium, 2002], that a complex-exponential modulated filter bankis an excellent tool for spectral envelope adjustment of audio signals.One application of this feature is audio coding based on Spectral BandReplication (SBR). Other fruitful applications of a complex filter bankinclude frequency selective panning and spatialization for parametricstereo, see [E. Schuijers, J. Breebart, H. Purnhagen, J. Engdegård: “Lowcomplexity parametric stereo coding”, Proc. 116^(th) AES convention,2004, paper 6073] and parametric multichannel coding, see [J. Herre etal.: “The reference model architecture for MPEG spatial audio coding”,Proc. 118^(th) AES convention, 2005, paper 6447]. In those applicationsthe frequency resolution of the complex filter bank is further enhancedat low frequencies by means of sub-subband filtering. The combinedhybrid filter bank hereby achieves a frequency resolution that enablesthe processing of spatial cues at a spectral resolution which closelyfollows the spectral resolution of the binaural auditory system. Theadditional filtering introduces no aliasing in itself, even ifmodifications are applied, so the quality of the hybrid filter bank isdetermined by the aliasing properties of the first filter bank.

If restraints on computational complexity prevent the usage of a complexexponential modulated filter bank, and only allows for a cosinemodulated (real-valued) implementation, severe aliasing is encounteredwhen the filter bank is used for spectral envelope adjustment. As shownin [O. Shamida et al.: “A low power SBR algorithm for the MPEG-4 audiostandard and its DSP implementation”, Proc. 116^(th) AES convention,2004, paper 6048] adaptive subband gain grouping (or gain locking) canalleviate the aliasing to some extent. However, this method works bestwhen only high frequency components of the signal have to be modified.For panning purposes in parametric multichannel coding, the amount ofgain locking necessary to render the aliasing at lower frequenciesinaudible will strongly reduce the frequency selectivity of the filterbank tool and will in practice render the additional frequencyselectivity of a hybrid filter bank unreachable. The result is a rathernarrow sound impression and problems with correct sound sourceplacement. A much better compromise between quality and complexity wouldbe obtained if the complex signal processing could be kept only for theperceptually more important lower frequencies.

SUMMARY OF THE INVENTION

It is the object of the present invention to provide a more efficientconcept for providing a signal allowing a manipulation with betterquality and a more efficient concept for reducing a signal with lessdistortions.

The present invention describes an apparatus for processing a pluralityof real-valued subband signals, the plurality of real-valued subbandsignals comprising a first real-valued subband signal and a secondreal-valued subband signal to provide at least a complex-valued subbandsignal, comprising a multiband filter for providing an intermediatereal-valued subband signal by filtering the first subband signal toprovide a first filtered subband signal and the second real-valuedsubband signal to obtain a second filtered subband signal and bycombining the first and the second filtered subband signals to providethe real-valued intermediate subband signal and a calculator forproviding the complex-valued subband signal by combining a real-valuedsubband signal from the plurality of real-valued subband signals as thereal part of the complex-valued subband signal and the intermediatesubband signal as an imaginary part of the complex-valued subbandsignal.

As a second aspect of the present invention, the present inventiondescribes an apparatus for processing a plurality of complex-valuedsubband signals, the plurality of complex-valued subband signalscomprising a first complex-valued subband signal and a secondcomplex-valued subband signal to obtain a real-valued subband signal,comprising an extractor for extracting from the first complex-valuedsubband signal a first imaginary part for extracting from the secondcomplex-valued subband signal a second imaginary part and for extractingfrom the first, the second or a third complex-valued subband signal ofthe plurality of complex-valued subband signals a real part, a multibandfilter for providing a real-valued intermediate subband signal byfiltering the first imaginary part to provide a first filtered imaginarypart signal, by filtering the second imaginary part to provide a secondfiltered imaginary part signal and by combining the first and the secondfiltered imaginary part signals to provide the intermediate subbandsignal, and a calculator for providing the real-valued subband signal bycombining the real part signal and the intermediate signal.

The present invention is based on the finding that a plurality ofreal-valued subband signals can be processed to provide at least onecomplex-valued subband signal allowing a manipulation with a betterquality than a manipulation of the plurality of real-valued subbandsignals, wherein a computational complexity of the processing of theplurality of real-valued subband signals is only slightly increased. Tobe more precise, the present invention is based on the fact that aplurality of real-valued subband signals can be processed by a multibandfilter and by a calculator to obtain a complex-valued subband signalwhich can be manipulated far more easily without creating a significantnumber of distortions and minimal aliasing as compared to directlymanipulating the plurality of real-valued subband signals.

In one embodiment of the present invention, an inventive apparatus forprocessing a plurality of real-valued subband signals is described,which provides a plurality of complex-valued subband signals from asubset of the plurality of real-valued subband signals, wherein a secondsubset of the plurality of real-valued subband signals is provided as afurther plurality of real-valued subband signals without being processedinto a corresponding number of complex-valued subband signals. Hence,this embodiment represents a partially complex modulated analysis filterbank, wherein the complex-valued subband signals will have the sameadvantages as corresponding subband signals from a complex exponentiallymodulated filter banks in terms of stability of energy estimation atminimal aliasing arising from linear time invariant modifications suchas a level of adjustment and further filtering. Furthermore, as anadditional advantage, the computational complexity as compared with acomplex filter bank for processing complex-valued signals issignificantly reduced.

As will be explained later, further embodiments of the present inventioncan also comprise modifications and modifier introducing time varianceand/or non-linear manipulations. Examples for such embodiments come fromthe fields of high quality SBR, varying applications of spatialparameters and other applications. In these embodiments, alladvantageous properties of the manipulators of the corresponding complexbank are present in the complex part of the partially complex filterbank of the embodiments of the present invention.

In a further embodiment of the present invention the further pluralityof real-valued subband signals, passed on by the inventive apparatus forprocessing the plurality of real-valued subband signals is delayed by adelayer to ensure a timely synchronicity with respect to thecomplex-valued subband signals output by the inventive apparatus.

The second aspect of the present invention is based on the finding thata plurality of complex-valued subband signals can be more efficientlyreduced to a real-valued subband signal with less distortions andminimal aliasing by extracting from at least two complex-valued subbandsignals real-valued imaginary parts of the at least two complex-valuedsubband signals and by extracting from the first, the second or a thirdcomplex-valued subband signal a real part by an extractor, by amultiband filter for providing an intermediate signal based on theimaginary parts and by a calculator for providing the real-valuedsubband signal by combining the real part signal and the intermediatesignal. To be more precise, the present invention is based on thefinding that prior to an optional real synthesis another multibandfilter converts the complex-valued subband signals back to real-valuedsubband signals, wherein the overall quality of reconstruction andsignal processing behavior is in line with that of a complex filterbank.

Depending on the concrete implementations of the embodiments, theextractor can also be implemented as a separator, if for instance morethan just one real-valued subband signal is to be provided. In this caseit might be useful to extract from all complex-valued subband signalstheir appropriate real parts and imaginary parts for further processing.

On the contrary, even if only a single real-valued subband signal is tobe obtained based on three or more different complex-valued subbandsignals, the extractor can be implemented as a separator, whichseparates each complex-valued subband signal into both its real partsand imaginary parts. In this case, the imaginary part signals and thereal part signals not required in the further process can simply beneglected. Hence, the terms separator and extractor can be synonymouslyused in the framework of the present application.

Furthermore, in the frame work of the present application, imaginarypart signals and imaginary parts as well as real parts and real partsignals refer to both signals having values, which correspond to eitheran imaginary part or a real part of a value of complex subband signals.In this context, it should also be noted that in principle both, anyimaginary part signal and any real part signal can be either real-valuedor complex-valued.

In one embodiment of the present invention, an inventive apparatus forprocessing a plurality of complex-valued subband signals is alsoprovided with a plurality of real-valued subband signals, wherein theplurality of complex-valued subband signals is processed as described inthe above terms and wherein the plurality of real-valued subband signalsis provided in an unfiltered form at an output of the apparatus. Hence,this embodiment forms a partially complex modulated synthesis filterbank. A major advantage of this embodiment is that the overall qualityof reconstruction and signal processing behavior is in line with that ofa complex filter bank with respect to the plurality of complex-valuedsubband signals and in line with that of a real filter bank in theremaining frequency range represented by the plurality of real-valuedsubband signals. As an additional advantage of the embodiments, thecomputational complexity is only slightly increased compared to that ofa real-valued filter bank. Furthermore, as an additional advantage ofthe embodiments a seamless transition between the two frequency rangesrepresented by both, the plurality of complex-valued subband signals andthe plurality of real-valued subband signals arises from a particularedge band treatment. Furthermore, as an additional advantage, thecomputational complexity as compared with a complex filter bank forprocessing complex-valued signals is significantly reduced.

A further embodiment of the present invention describes a system whichcombines both, an inventive apparatus for processing a plurality ofreal-valued subband signals and an inventive apparatus for processing aplurality of complex-valued subband signals, wherein both inventiveapparatuses also pass on a further plurality of real-valued subbandsignals. In between the two inventive apparatuses a first and a secondmanipulator modify the plurality of complex-valued subband signalsoutput by the inventive apparatus for processing a plurality ofreal-valued subband signals and modify the further plurality ofreal-valued subband signals, respectively. The first and the secondmanipulator can perform linear time invariant modifications such as anenvelope adjustment or a filtering. As a consequence, in the systemdescribed, the overall quality of reconstruction and signal processingbehavior is with respect to the frequency range represented by theplurality of complex-valued subband signals in line with that of acomplex filter bank and with respect to the frequency range representedby the further plurality of real-valued subband signals in line withthat of a real filter bank, leading to a manipulation of the signalswith a far better quality as compared to directly modifying theplurality of real-valued subband signals, while the computationalcomplexity is only slightly increased. As outlined before and moreclosely explained later, the manipulators of other embodiments are notlimited to linear and/or time invariant manipulations.

In a further embodiment of the inventive apparatus for processing aplurality of complex-valued subband signals a further plurality ofreal-valued subband signals is passed on in a delayed form by employinga delayer to ensure a timely synchronicity with respect to thereal-valued subband signal output by the inventive apparatus forprocessing a plurality of complex-valued subband signals.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described by way of illustrativeexamples, not limiting the scope or spirit of the invention, withreference to the accompanying drawings. Preferred embodiments of thepresent invention are subsequently described by the following drawings,wherein:

FIG. 1 illustrates partially complex signal processing;

FIG. 2 illustrates a partially complex analysis filter bank;

FIG. 3 illustrates a partially complex synthesis filter bank;

FIG. 4 illustrates multiband filtering;

FIG. 5 illustrates the spectrum of an original signal containingmultiple sinusoidal components;

FIG. 6 illustrates the spectrum of a signal obtained by analysis andsynthesis without subband modification in a partially complex filterbank that does not incorporate the seamless transition feature taught bythe current invention;

FIG. 7 illustrates the spectrum of a signal obtained by modification inthe subband domain of a complex filter bank;

FIG. 8 illustrates the spectrum of a signal obtained by modification inthe subband domain of a real filter bank;

FIG. 9 illustrates the spectrum of a signal obtained by modification inthe subband domain of a partially complex filter bank as taught by thecurrent invention;

FIG. 10 illustrates a hybrid QMF analysis bank for a time/frequencytransform in spatial audio coding;

FIG. 11 illustrates a hybrid QMF synthesis bank for a time/frequencytransform in spatial audio coding;

FIG. 12 shows a flowchart of a real-valued analysis QMF bank;

FIG. 13 shows an embodiment of an inventive apparatus for processing aplurality of real-valued subband signals as a real to complex converter;and

FIG. 14 shows an embodiment of an inventive apparatus for processing aplurality of complex-subband signals in the form of a complex to realconverter.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The below-described embodiments are merely illustrative for theprinciples of the present invention of a partially complex modulatedfilter bank. It is understood that modifications and variations of thearrangements and the details described herein will be apparent to othersskilled in the art. It is the intent, therefore, to be limited only bythe scope of the impending patent claims and not by the specific detailspresented by way of description and explanation of the embodimentsherein.

FIG. 1 illustrates the principle of partially complex signal processingbased on a partially complex analysis 101 and synthesis 104 filterbanks. A digital audio input signal is fed into to the partially complexanalysis filter bank 101. Out of a total of L subband signals, thisanalysis bank outputs K complex and (L-K) real subband signals, whereinK and L are positive integers and K≦L. A first modification 102 isperformed on the real subband signals and a second modification 103 isperformed on the complex signals. These modifications both aim atshaping the audio signal in time and frequency. The modified subbandsignals are subsequently fed into a partially complex synthesis filterbank 104 which produces as output the processed digital audio signal.

FIG. 2 illustrates the components of an embodiment of a partiallycomplex analysis filter bank 101 as taught by the present invention. Thedigital audio input signal is analyzed by an L-band cosine modulatedfilter bank 201 which at the output splits the L real subband signalsinto two groups. The first group consisting of K real subband signals isfiltered by the multiband filter 204 whose output is multiplied by thenegative of the imaginary unit in the multiplier 205 and added in 206 tothe K real subband signals delayed by 203 in order to produce K complexsubband signals. Those subband signals are gain adjusted by a fixed realgain 207 and output as the K complex subbands of the partially complexanalysis. The second group consisting of (L-K) real subband signals arefed to the delay unit 202 whose output constitutes the real subbands ofthe partially complex analysis.

The amount of delay in both 202 and 203 is adjusted in order tocompensate for the delay introduced by the multiband filter 204. Thedelayer 202, the delayer 203, the multiband filter 204, the multiplier205, the adder 206 and the fixed real gain adjustment 207 form a real tocomplex converter 210, which is provided with a plurality of Kreal-valued subband signals and a further plurality of (L-K) real-valuedsubband signals providing K complex-valued subband signals and (L-K)real-valued subband signals. Furthermore, the multiplier 205 and theadder 206 form a calculator 215, which provides at least onecomplex-valued subband signal based on at least one real-valued subbandsignal as a real part signal and on at least one real-valued subbandsignal as an imaginary part of the complex-valued subband signal.

FIG. 3 illustrates the components of an embodiment of a partiallycomplex synthesis filter bank 104 as taught by the present invention.The (L-K) real subband signals are simply delayed in 304 and fed into(L-K) inputs of the L-band cosine modulated synthesis filter bank 308.The K complex subbands are first gain adjusted by a fixed real gain 301.Then the real and the imaginary parts of the complex subband signals areextracted in 302 and 303 respectively. The imaginary parts of thesubbands are filtered by the multiband filter 306 whose output is addedin 307 to the real parts of the subbands delayed by 305. The amount ofdelay in both 304 and 305 is adjusted in order to compensate for thedelay introduced by the multiband filter 306. The output of the adder307 is fed into remaining K inputs of the L-band cosine modulatedsynthesis filter bank 308. The real part extractor 302 and the imaginarypart extractor 303 together form a separator 309 for separating acomplex-valued subband signal into a real-valued real part signal andthe real-valued imaginary part signal. To be more precise, the real partextractor 302 provides the real part signal and the imaginary partextractor 303 provides the imaginary part signal. In a specialembodiment shown in FIG. 3, the separator 309 processes or ratherseparates K complex-valued subband signals into K real-valued real partsignals and K real-valued imaginary part signals.

Nevertheless, as described above, the separator 309 can also beimplemented as an extractor, which is adapted for not separating allcomplex-valued subband signals into real part signals and imaginary partsignals. Hence, the separator 309 is also synonymously referred to asextractor 309 for extracting real part signals (real parts) andimaginary part signals (imaginary parts) from complex-valued subbandsignals.

The fixed real gain adjuster 301, the separator 309, which comprises thereal part extractor 302 and the imaginary part extractor 303, thedelayer 304, the delayer 305, the multiband filter 306 and the adder 307together form an inventive complex to real converter 310, which iscapable of converting K complex-valued subband signals into Kreal-valued subband signals and providing (L-K) real-valued subbandsignals in a is delayed form at an output of the complex to realconverter 310.

FIG. 4 illustrates the operation of a multiband filter 401 that takes Kreal subband signals as inputs 0, 1, 2, . . . , (K−1) and gives K realsubband signals as outputs 0, 1, 2, . . . (K−1). In the language oflinear systems this is simply a linear time invariant discrete-timemultiple input multiple output (MIMO) system. The m th output isproduced in 402 m by filtering the (q(m)+p(m)+1) inputs (m−q(m)), . . ., m, . . . , (n+p(m)) with the filters F_(m,−q(m)), . . . , F_(m,0), . .. , F_(m,+p(m)) respectively and summing the results in 403 m. Theconstraints (m−q(m))≧0 and (m+p(m))≦K−1 must hold. As outlined in thefollowing description, the present invention teaches how to obtain acomplex representation of high quality by using multiband filters 204and 306 of low computational complexity that have

$\begin{matrix}{{{q(m)} = \begin{Bmatrix}{0,} & {{{for}\mspace{14mu} m} = 0} \\{1,} & {{{{for}\mspace{14mu} m} = 1},\ldots\mspace{11mu},{K - 1}}\end{Bmatrix}},{and}} & (1) \\{{p(m)} = {\begin{Bmatrix}{1,} & {{{{for}\mspace{14mu} m} = 0},\ldots\mspace{11mu},{K - 2}} \\{0,} & {{{for}\mspace{14mu} m} = {K - 1}}\end{Bmatrix}.}} & (2)\end{matrix}$

Moreover, similarities of the filters F_(m,−1) and F_(m,1) can beexploited to reduce complexity even further.

The particularly small values of q(m) and p(m) as described by (1) and(2) can be used when prototype filter of the cosine modulated filterbank has a sufficiently high degree of stop band attenuation. Thisimplicitly requires a certain minimal length of prototype filter. Forshorter prototype filters, the values of q(m) and p(m) have to beincreased. However, the method taught by the present invention remainscomputationally efficient since the length of filters F_(m,r) isproportional to the length of the prototype filter.

The filters implemented in the multiband filter 401 can be in principleall kinds of filters with all kinds of filter characteristics. In theembodiment shown in FIG. 4, the multiband filter F_(m,0), that maps asubband signal with the index m into a subband signal with the samesubband index m is typically a bandpass filter with a center frequencyat (π/2). In the case of a multiband filter combining three subbandsignals into one subband signal as a filterbank signal, the other twomultiband filters F_(m,−q(m)) and F_(m,+p(m)) are typically either highpass or low pass filters, wherein their exact type depends on thesubband index m. If the multiband filter 401 is adapted to combiningmore than three subband signals to obtain the filter subband signalswith an index m, which is not “border” subband signal, the correspondingtypes of multiband filters can be bandpass filters, high pass filters,low pass filters, band stop filters or all pass filters.

The embodiments shown in FIGS. 1-3 hence describe a method formodification of a discrete-time audio signal, characterized by:

-   -   Filtering the signal by a cosine modulated analysis filter bank,    -   creating complex subband samples for a subset of the subbands by        means of multiband filtering,    -   modifying both the real and the complex subband samples,    -   transforming the resulting complex samples to real samples by        means of a multiband filtering,    -   filtering the real subband samples through a cosine modulated        synthesis filter bank.

FIG. 5 illustrates a part of the magnitude spectrum of an originalsignal containing multiple sinusoidal components. This spectrum isobtained by the use of a windowed discrete Fourier transform. Thefrequency axis is normalized such that the frequency index n correspondsto a discrete-time frequency equal to (nπ/L) with L=64. Hence, if thesampling frequency of the digital audio signal is f_(s), the frequencyrange shown in FIG. 5 goes from (5/64)·f_(s)/2 to (11/64)·f_(s)/2. Inthis normalization, the subband with index n of a complex or realmodulated filter bank with L subbands has a response with main lobecentered between frequency index n and (n+1). This convention is keptfor all of the FIGS. 5-9.

In other words, each subband or subband signal is associated with both,an index n or m and a center frequency of the corresponding subband.Hence, the subband signals or rather the subbands can be arrangedaccording to the center frequencies associated with the subband signalsin such a way that an increasing index can, for example, correspond to ahigher frequency.

FIG. 6 illustrates the spectrum of a signal obtained by analysis andsynthesis without subband modification in a partially complex filterbank that does not incorporate the seamless transition feature taught bythe current invention. Specifically, a more naïve approach is consideredwhere 101 constructed out of two filter banks with L=64 subbands, thefirst bank is complex exponential modulated and the second bank iscosine modulated. Both filter banks yield near perfect reconstructionwhen used separately. The construction considered here takes the K=8first subbands from the first complex bank and the (L-K)=56 remainingsubbands from the second real bank. The input signal is identical to thesignal considered in FIG. 5, and as it can be seen by comparison to FIG.5, an alias component has been introduced near frequency index 8, whichmarks the transition frequency between complex and real subbands.Disregarding for a moment that the complexity of this naïve approach isin fact higher than for a single complex bank, the example shows thatthere is a need for a special handling of the transition between complexand real subbands. The case where no modifications are performed in 102and 103 should preferably give rise to a digital audio output from 104which is perceptually indistinguishable from the input to 101. Thepartially complex analysis and synthesis filter banks described by thepresent invention as in FIGS. 2 and 3 possess exactly that feature. Inparticular, the corresponding magnitude spectrum of the processed signalis identical to that of FIG. 5. Hence a concatenation of a multibandanalysis filter or an analysis filter bank and a synthesis multibandfilter or a synthesis filter bank, in other words a concatenation of amultiband analysis and synthesis filtering, should lead to near perfectreconstruction, e.g. up to a sign change.

FIG. 7 illustrates the spectrum of a signal obtained by modification inthe subband domain of a complex exponential modulated filter bank. Themodification consists of applying a gain g(n) to the subband with indexn, where g(n) is a decreasing function of n. Compared to FIG. 5, thesinusoidal components have simply changed magnitudes accordingly. Thisdescribes the desired behavior of an equalization or envelope adjustmentof the original signal. Performing the same modification with a realcosine modulated filter bank leads an output signal with the frequencyanalysis depicted on FIG. 8. Additional aliased sinusoidal componentsmake the result deviate considerably from the desired behavior asdescribed by FIG. 7 and the distortion is audible. Applying the samegain modification in a partially complex filter bank as taught by FIGS.2 and 3 realized by multiband filters as in FIG. 4 with 11 filter tapsfor each individual filter leads to the magnitude spectrum of FIG. 9.Again K=8 is chosen and as it can be seen, the output has the quality ofcomplex filter bank processing (FIG. 7) below the frequency indexK−0.5=7.5 and the quality of the real filter bank processing (FIG. 8)above this frequency index.

Hence, the present invention relates to systems comprising equalization,spectral envelope adjustment, frequency selective panning, or frequencyselective spatialization of audio signals using a downsampledreal-valued subband filter bank. It permits suppression of aliasing fora selected frequency range by transforming a corresponding subset ofsubband signals into complex-valued subband signals. Assuming that thealiasing outside the selected frequency range is less noticeable or canbe alleviated by other methods, this permits large savings incomputational effort in comparison to the use of a complex-valued filterbank.

Modulated Filter Banks

For ease of computations a complex exponential modulated L-band filterbank will be modeled here by a continuous time windowed transform usingthe synthesis waveformse _(n,k)(t)=e _(n)(t−k),  (3)where n,k are integers with n≧0 ande _(n)(t)=e _(n,0)(t)=ν(t)exp[iπ(n+½)(t+½)].  (4)

The window function ν(t) is assumed to be real valued. By splittinge_(n)(t)=c_(n)(t)+is_(n)(t) into real and imaginary parts, one obtainsthe synthesis waveforms for cosine and sine modulated filter banks,

$\begin{matrix}{\begin{Bmatrix}{{c_{n,k}(t)} = {c_{n}\left( {t - k} \right)}} \\{{s_{n,k}(t)} = {s_{n}\left( {t - k} \right)}}\end{Bmatrix}.} & (5)\end{matrix}$

Results for discrete-time signals and filter banks with L subbands areobtained by suitable sampling of the t-variable with spacing 1/L. Definethe inner product between signals by

x, y

=∫_(−∞) ^(∞) x(t)y*(t)dt  (6)where the star denotes complex conjugation. For discrete-time signalsthe integral is replaced by a summation. The operation of a cosine andsine modulated filter bank analysis of a signal x(t) is then describedbyα_(n)(k)=

x,c _(n,k)

, β_(n)(k)=

x,s _(n,k)

.  (7)

Given subband signals {tilde over (α)}_(n), {tilde over (β)}_(n), thecorresponding synthesis operations are

$\begin{matrix}{{{y_{c}(t)} = {\sum\limits_{n = 0}^{\infty}{\sum\limits_{k = {- \infty}}^{\infty}{{{\overset{\sim}{\alpha}}_{n}(k)}{c_{n,k}(t)}}}}},{{y_{s}(t)} = {\sum\limits_{n = 0}^{\infty}{\sum\limits_{k = {- \infty}}^{\infty}{{{\overset{\sim}{\beta}}_{n}(k)}{s_{n,k}(t)}}}}}} & (8)\end{matrix}$

For discrete-time signals, the summation over the subband index n islimited to (L−1). It is well known from the theory of cosine/sinemodulated filter banks and lapped transforms that the window functionν(t) can be designed such that the combined analysis and synthesisoperations lead to perfect reconstruction y_(c)=y_(s)=x for unmodifiedsubband signals {tilde over (α)}_(n)=α_(n), {tilde over (β)}=β_(n). Fornear perfect reconstruction designs, those equalities will beapproximate.

The operation of a complex exponential modulated filter bank as taughtby PCT/SE02/00626 “Aliasing reduction using complex exponentialmodulated filter banks” can be described by the complex analysis,γ_(n)(k)=g _(a)

x,e _(n,k)

=g _(a)(α_(n)(k)−iβ _(n)(k)),  (9)where g_(a) is a fixed real analysis gain factor. The synthesis fromcomplex subband signals {tilde over (γ)}_(n)={tilde over(α)}_(n)−i{tilde over (β)}_(n) is defined by

$\begin{matrix}{\begin{matrix}{{y_{e}(t)} = {g_{s}\;{Re}\left\{ {\sum\limits_{n = 0}^{\infty}\;{\sum\limits_{k = {- \infty}}^{\infty}\;{{{\overset{\sim}{\gamma}}_{n}(k)}{e_{n,k}(t)}}}} \right\}}} \\{{= {g_{s}g_{a}{\sum\limits_{n = 0}^{\infty}{\sum\limits_{k = {- \infty}}^{\infty}\left( {{{{\overset{\sim}{\alpha}}_{n}(k)}{c_{n,k}(t)}} + {{{\overset{\sim}{\beta}}_{n}(k)}{s_{n,k}(t)}}} \right)}}}},}\end{matrix}} & (10)\end{matrix}$where g_(s) is a fixed real synthesis gain factor. Assuming that thecomplex subband signals are unmodified {tilde over (γ)}_(n)=γ_(n) andthat the cosine and sine modulated banks have perfect reconstruction,one finds from (8) and (9) thaty _(e) =g _(s) g _(a)(y _(c) +y _(s))=2g _(s) g _(a) x.  (11)

Hence perfect reconstruction is achieved ifg _(a)g_(s)=1/2.  (12)

A particularly attractive choice of fixed gains leading to energypreservation of the complex subband representation isg_(a)=g_(s)=1/√{square root over (2)}.

It is immediate that in the complex case, deviations from the specificmodulation described by (4) by a fixed phase factor for each subband canbe permitted without changing the reconstruction properties, since themodification of the complex subband signals in (9) and (10) will cancelout. The complex exponential modulated filter bank is oversampled by afactor of two. With a proper window design, this enables virtually aliasfree envelope adjustment as shown in PCT/SE02/00626 “Aliasing reductionusing complex exponential modulated filter banks”. Such designs areoften easier to achieve by abandoning the strictly perfectreconstruction framework described above in favor of near-perfectreconstruction.

Multiband Filtering

Assuming that only the cosine modulated bank analysis α_(n)(k) of (7) isavailable, the corresponding sine modulated bank analysis β_(m)(l) canbe obtained by combining a cosine bank synthesis step and a sine bankanalysis. One finds that

$\begin{matrix}{{{\beta_{m}(l)} = {\sum\limits_{n = 0}^{\infty}\;{\sum\limits_{k = {- \infty}}^{\infty}{{\alpha_{n}(k)}\left\langle {c_{n,k},s_{m,l}} \right\rangle}}}},} & (13)\end{matrix}$where a change of time variable in the inner product leads to

c _(n,k) ,s _(m,l)

=

c _(n) ,s _(m,l−k)

.  (14)

Hence the summation with respect to k in (13) corresponds to a filteringand the overall structure is recognized as a version of the multibandfiltering depicted in FIG. 4 with infinitely many bands. A re-writing interms of the complex waveforms (4) yields

$\begin{matrix}{\left\langle {c_{n},s_{m,\lambda}} \right\rangle = {\frac{1}{2}{Im}{\left\{ {\left\langle {e_{m,\lambda},e_{n}} \right\rangle + \left\langle {e_{m,\lambda},e_{{- 1} - n}} \right\rangle} \right\}.}}} & (15)\end{matrix}$

After a substitution t→t+μ/2, the first term of (15) can be expandedinto

$\begin{matrix}{\left\langle {e_{m,\lambda},e_{n}} \right\rangle = {{\exp\left\lbrack {{\mathbb{i}}{\frac{\pi}{2}\left\lbrack {m - n - {\left( {m + n + 1} \right)\lambda}} \right\rbrack}} \right\rbrack}{\int_{- \infty}^{\infty}{{v\left( {t - {\lambda/2}} \right)}{v\left( {t + {\lambda/2}} \right)}{\exp\left\lbrack {{\mathbb{i}}\;{\pi\left( {m - n} \right)}t} \right\rbrack}\ {{\mathbb{d}t}.}}}}} & (16)\end{matrix}$

With a symmetric window ν(−t)=ν(t), the imaginary part of the integralin (16) vanishes, such that

$\begin{matrix}{{{{Im}\left\langle {e_{m,\lambda},e_{n}} \right\rangle} = {{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {m - n - {\left( {m + n + 1} \right)\lambda}} \right\rbrack} \right\rbrack}{h_{m - n}(\lambda)}}},} & (17)\end{matrix}$with the definition

$\begin{matrix}{{h_{\mu}(\lambda)} = {\int_{- \infty}^{\infty}{{v\left( {t - {\lambda/2}} \right)}{v\left( {t + {\lambda/2}} \right)}{\cos\left\lbrack {\pi\;\mu\; t} \right\rbrack}\ {{\mathbb{d}t}.}}}} & (18)\end{matrix}$

This expression is an even function of both μ and λ. For suitabledesigns of windows one can assume that h_(μ) vanishes for |μ|>1. In thediscrete-time case, the integral in (18) is to be replaced by asummation over integers ν′ with t=(ν+θ)/L, where L is the number ofsubbands and θ is an offset value either equal to 0 or ½. Thediscrete-time counterpart of (18) is periodic in μ with period 2L forθ=0 and antiperiodic in μ with period 2L for θ=½. Inserting n=m+r in(15) yields

$\begin{matrix}{\left\langle {c_{m + r},s_{m,\lambda}} \right\rangle = {\frac{1}{2}{\left\{ {{{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {{- r} - {\left( {{2\; m} + 1 + r} \right)\lambda}} \right\rbrack} \right\rbrack}{h_{r}(\lambda)}} + {{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {{r\;\lambda} + {2m} + 1 + r} \right\rbrack} \right\rbrack}{h_{{2\; m} + 1 + r}(\lambda)}}} \right\}.}}} & (19)\end{matrix}$

Referring to 402 m in FIG. 4, f_(m,r)(λ)=

c_(m+r),s_(m,λ)

can be used as the impulse response of the filter F_(m,r) if L=K isinserted in the above computations. Assuming h_(μ) vanishes except forμ=2Kκ+σ where κ is an integer and σε{−1, 0, 1}, it follows that thesecond term of (19) only gives a contribution for m=0 and m=(K−1). Theseedge cases are important since they contain the key to nearinvertibility of the multiband filter 401. Apart from the trivialmodulations of (19), only two prototype filters h₀, h₁ have to beconsidered, and an inspection of (19) shows that only the odd samples ofh₀ come into play. Moreover it is clear for those skilled in the artthat the special modulations of (19) and the similarity of the filtersf_(m+1,−1), and f_(m−1,1) allows for a very efficient implementation ofthe multiband filter in polyphase form. A more detailed description ofsuch an embodiment will be presented in the further course of thisapplication.

For practical designs it is advantageous to abandon the discretizedinner product (18) for the design of those prototype filters. Instead,for a chosen integer N the filters f_(m,r) are designed to give the bestapproximation

$\begin{matrix}{s_{m} \approx {\sum\limits_{r}^{\;}{\sum\limits_{k = {- N}}^{N}{{f_{m,r}\left( {- k} \right)}{c_{{m + r},k}.}}}}} & (20)\end{matrix}$

This gives a second, more direct path to the sine modulated bankanalysis

$\begin{matrix}{\beta_{m} = {\sum\limits_{r = {- 1}}^{1}{f_{m,r}*\alpha_{m + r}}}} & (21)\end{matrix}$where the star denotes convolution. Moreover, expanding the sinesynthesis operation (8) by inserting (20) and collecting the cosineterms leads to

$\begin{matrix}{{{{\overset{\sim}{a}}_{n}(k)} = {\sum\limits_{r,l}{{f_{{n - r},r}\left( {l - k} \right)}{{\overset{\sim}{\beta}}_{n - r}(l)}}}},} & (22)\end{matrix}$such that the synthesis multiband filter 306 also has the structure of401 with filters replaced by G_(m,r) with impulse responsesg_(m,r)(λ)=f_(m+r,−r)(−λ). The same result would also follow frominterchanging the role of cosine and sine modulation in the derivationsabove.

The total computational complexity of the multiband filter isproportional to N·K operations per subband sample period, that is, N·K/Loperations per digital audio sample. When K<<L this leads to aconsiderable saving in comparison to additional sine modulation requiredfor a full complex modulated filter bank.

Compared to the application of a purely real or purely complex modulatedfilter bank and additional delay of N subband samples is introduced bythe multiband filter in both the analysis and the synthesis step. Thisis compensated for by delaying all the subband samples which do not passthe multiband filter by a delay of N subband samples in 202, 203, 304,and 305. In the case where the modification 103 comprises a sub-subbandfiltering as described in [E. Schuijers, J. Breebart, H. Purnhagen, J.Engdegård: “Low complexity parametric stereo coding”, Proc. 116^(th) AESconvention, 2004, paper 6073], the sub-subband filters can be combinedwith the multiband filter 204 in order to enable a reduction of thetotal delay by means of approximating the combined impulse responses.

If the selected K complex subbands are the first K of a total of Lsubbands, the multiband filter emulates the effect of a synthesis of afilter bank with K subbands to a time domain of K/L times the originalsampling frequency followed by an analysis with a filter bank with Ksubbands. Such a detour has the disadvantage of leading to a longermultiband filter delay than what can be achieved with the design methodtaught by the current invention. For applications where the number ofanalysis audio channels are much smaller than the number of synthesischannels, the analysis delay of the multiband filter can be avoidedaltogether at the price of higher computational complexity simply byperforming the partially complex analysis 101 by a true complexmodulated filter bank analysis with L subbands and discarding theimaginary part of the last (L-K) subbands. However, in order to make thecombination with the synthesis of FIG. 3 lead to near perfectreconstruction in the case of unaltered subbands it is necessary toreplace the analysis of the edge subband with index (K−1) with a specialdirect form filter followed by subsampling by a factor L. Hence, thisfilter can be obtained by studying the partially complex synthesis ofFIG. 3 in the case where the edge subband with index (K−1) contains onlyone nonzero sample and all other subbands are zero. Although of lessusefulness in terms of complexity reduction, the synthesis delay of themultiband filter can be avoided similarly by performing the partiallycomplex synthesis 104 by a true complex modulated filter bank synthesiswith L subbands for which the input subband with index (K−1) isredirected to a separate synthesis operation consisting of upsampling bya factor L followed by a special direct form filtering. The results ofthe complex bank synthesis from (L−1) bands and the separate one bandsynthesis are then added in the time domain.

The present invention relates to systems comprising equalization,spectral envelope adjustment, frequency selective panning, or frequencyselective spatialization of audio signals using a downsampledreal-valued subband filter bank. It permits suppression of aliasing fora selected frequency range by transforming a corresponding subset ofsubband signals into complex-valued subband signals. Assuming that thealiasing outside the selected frequency range is less noticeable or canbe alleviated by other methods, this permits large savings incomputational effort in comparison to the use of a complex-valued filterbank.

The present invention teaches how to obtain complex representation of asignal for a selected frequency range, at a computational complexitywhich is only slightly larger than that of a real-valued filter bank. Anefficient multiband filter is applied to selected subbands of the realfilter bank analysis in order to produce imaginary parts of thosesubband signals. The result is a partially complex modulated filter bankanalysis. The complexified subbands will have the same advantages as thecorresponding subbands from a complex exponentially modulated filterbank in terms of stability of energy estimation and minimal aliasingarising from linear time invariant modifications such as envelopeadjustment and filtering. Prior to the real synthesis, another multibandfilter converts the complex subband samples back to real subbandsamples. The overall quality of reconstruction and signal processingbehavior is in line with that of a complex filter bank in thecomplexified frequency range and in line with that of a real filter bankin the remaining frequency range. A seamless transition between the tworanges arises implicitly from a particular edge band treatment taught bythe present invention.

In the frame work of the modifiers or manipulators 102, 103 time varyingapplication of spatial parameters (e.g. MPEG Surround or parametricstereo) by means of time interpolated gains or matrices should bementioned. In the case of time invariant modifications or manipulations,the application to envelope adjustment or equalization with a feature tonot introduce aliasing is important. Hence, definitions concerning anintroduction of aliasing are mainly focused on time invariant cases.

Nevertheless, introducing time variance for instance in the frame workof the manipulators or modifiers 102, 103 shown in FIG. 1 represents acase in which the definition of the feature to not introduce aliasingbecomes more difficult. In practice, for instance long important piecesof signals will be treated in a locally time invariant manner even inthe frame work of MPEG Surround. In a further step, nonlinearmanipulations can also be considered for instance in the frame work ofadvanced transposition methods, like high-quality SBR, which will becomeimportant. Although these advanced transposition methods comprise timevariant and/or non-linear manipulations, in a first step time invariantmodifications and manipulations will have to be considered.

To summarize, in the frame work of the modifiers or manipulators 102,103, any manipulation is certainly possible and relevant as long as itrequires the time frequency resolution of the resulting (partiallycomplex) filter bank. Hence, all advantages of the manipulations 103 ofa corresponding complex bank are also present in the complex part of thepartially complex filter bank.

The embodiment of the present invention described in FIGS. 1-3 comprisesthe following features:

-   -   A method for modification of a discrete-time audio signal        comprising the steps of        -   filtering the signal by a cosine modulated analysis filter            bank,        -   creating complex subband samples for a subset of the            subbands by means of multiband filtering,        -   modifying both the real and the complex subband samples,        -   transforming the resulting complex samples to real samples            by means of multiband filtering,        -   filtering the real subband samples through a cosine            modulated synthesis filter bank to obtain a modified            discrete-time audio signal.

In the following sections an implementation of a low power version of aspatial audio tool is outlined. The low power spatial audio tooloperates on real-value subband domain signals above the K-th QMF subband(QMF=quadrature mirror-filter), wherein K is a positive integer. Theinteger K is chosen according to the specific needs and specificationsof the implementation intended. In other words, the integer K is givenby details of the intended implementation, such as a bitstream info. Areal-valued QMF filter bank is used in combination with an inventivereal to complex converter to achieve a partially complex subband domainrepresentation. Furthermore, the low-power spatial audio tool mayincorporate additional modules in order to reduce aliasing introduceddue to the real-valued processing.

Following this short introduction, the low power spatial audio codingsystem employs a time/frequency transform according to FIG. 10. Thetime/frequency transformer of the described spatial audio codingcomprises a hybrid QMF analysis bank shown in FIG. 10. The hybrid QMFanalysis bank to process a real QMF analysis bank 500 is connected viaan optional switch 510 to an inventive real to complex converter 520.The real to complex converter 520 is furthermore connected to one ormore Nyquist analysis banks 530.

The real QMF analysis bank 500 is at an input provided with time domaininput signals {tilde over (x)} and provides at an output real-valued QMFsignals {circumflex over (x)}_(real) ^(n,m) to the real to complexconverter 520. The real to complex converter 520 turns the QMF signalsinto partially complex samples {circumflex over (x)}^(n,m), which arethen provided to the Nyquist analysis banks 530, which in turn producehybrid subband domain signals x^(n,m).

Apart from the regular mode of operation of this time/frequencytransformer, wherein the spatial audio decoder is set with time domainsamples {tilde over (x)}, also (intermediate) real-valued (QMF) subbanddomain samples {circumflex over (x)}_(real) ^(n,m), for instance from alow-complexity HE-AAC decoder can be taken. To be more precise, in thatcase the subband domain samples prior to HE-AAC QMF synthesis are taken,as laid out in [ISO/IEC 14496-3:2001/AND1:2003]. To enable also theseQMF input signals {circumflex over (x)}_(real) ^(n,m) to be fed to theinventive real to complex converter 520, the optional switch 510 isintegrated into the time/frequency transformer shown in FIG. 10 andswitched accordingly.

The real QMF samples, either provided in the form of QMF input signalsor via the real QMF analysis bank 500, are converted to partiallycomplex samples {circumflex over (x)}^(n,m) by the real to complexconverter 520, which will be described in more detail with reference toFIG. 13 below. Furthermore, as an additional option and if enabled, aresidual decoding module not shown in FIG. 10 can provide subband domainsamples {circumflex over (x)}_(res) ^(n,m) as QMF residual inputsignals. These QMF residual signals are also passed on to the Nyquistanalysis banks 530 via an optional delayer 540, as these QMF residualinput signals may also need to be passed on in a delayed form in orderto compensate for a delay caused by the real to complex converter 520,before being transformed to the hybrid domain also forming hybridsubband domain signals x^(n,m.)

FIG. 11 shows a hybrid QMF synthesis bank for performing afrequency/time transform or rather a time/frequency transform in aspatial audio coding system. The hybrid QMF synthesis bank comprises oneor more Nyquist synthesis banks 550 to which a hybrid subband domainsignal y^(n,m) is provided at an input. To be more precise, at theNyquist synthesis side the hybrid subband domain samples y^(n,m) aretransformed to partially complex QMF subband domain samples ŷ^(n,m) bythe Nyquist synthesis banks 550. The partially complex QMF subbanddomain samples are then provided to an inventive complex to realconverter 560, which converts the partially complex QMF subband domainsamples into real-valued or rather real QMF samples ŷ_(real) ^(n,m). Theinventive complex to real converter 560 will be described in more detailin context with FIG. 14. Those real QMF samples are provided to a realQMF synthesis bank 570, where they are transformed back to the timedomain in the form of time domain samples or rather time domain outputsignals {tilde over (y)}.

The filter banks, or to be more precise, the real QMF analysis bank 500and the real QMF synthesis bank 570 will now be described in moredetail. For instance, for low power MPEG surround systems, real-valuedQMF filter banks are used. In this case, the analysis filter bank 500uses 64 channels as is outlined below. The synthesis filter bank 570also has 64 channels and is identical to the filter bank used in lowcomplexity HE-AAC systems as they are described in section 4.6.18.8.2.3of ISO/IEC 14496-3. Although the following description is based on 64channels (integer L=64), the present invention and its embodiments arenot limited to using 64 channels or an appropriate number of real-valuedor complex-valued subband signals. In principle, an arbitrary number ofchannels or rather real-valued or complex-valued subband signals can beused in context with embodiments of the present invention. However, if adifferent number of channels is used, the appropriate parameters of theembodiments would also have to be adapted accordingly. The real-valuedQMF analysis bank 500, shown in FIG. 10, is used to split the timedomain signal {tilde over (x)} from the core decoder into 64 subbandsignals. The output from the filter bank or rather the real-valued QMFbank 500 are real-valued and critically sampled signals in the form ofsubband samples.

FIG. 12 shows a flowchart of the operation performed by the real-valuedanalysis QMF bank 500 in the form of C/C++—pseudocode. In other words,the method performed by the real QMF analysis bank 500 is illustrated inFIG. 12. The filtering involves the following steps, wherein an array xcomprises 640 time domain input samples labeled with an index between 0and 639. In FIG. 12, indices of arrays or vectors are enclosed byrectangular brackets. A higher index into the array x of time domaininput samples corresponds to older sample.

FIG. 12 illustrates the method performed by the real QMF analysis bank500 for a QMF subband sample l. After starting the method in step S100,the samples in the array x are shifted in step S110 by 64 positions. Theoldest 64 samples with indices ranging from 575 to 639 (n=575, . . . ,639) are discarded. Afterwards, 64 new samples are stored in the array xin the positions with indices 0-63 in step S120.

In step S130 the samples of the array x are multiplied by a set ofcoefficients of a window or rather a window function c. The window c isalso implemented as an array c with 640 elements with indices rangingfrom n=0, . . . , 639. This multiplication is done in step S130 byintroducing a new intermediate array z with 640 elements according toz(n)=x(n)·c(n), n=0, . . . , 639  (23)wherein the window coefficients c[0], . . . , c[639] can be found inTable 4.A.87 of ISO/IEC 14496-3.

In a following step S140 the samples represented by the intermediatearray z are summed up according to

$\begin{matrix}{{{u(n)} = {\sum\limits_{j = 0}^{4}{z\left( {n + {j \cdot 128}} \right)}}},\mspace{14mu}{n = 0},\ldots\mspace{14mu},127} & (24)\end{matrix}$creating a new intermediate 128-element array u. Equation 24 is alsoshown in the flowchart of FIG. 12 as a mnemonic code representing theformula of Equation 24.

In the following step S150 new 64 subband samples are calculated by amatrix operation M·u with a matrix M, wherein the elements of the matrixM are given by

$\begin{matrix}{{{M_{r}\left( {k,n} \right)} = {2 \cdot {\cos\left( \frac{\pi \cdot \left( {k + 0.5} \right) \cdot \left( {{2 \cdot n} - 192} \right.}{128} \right)}}},\mspace{14mu}\left\{ \begin{matrix}{0 \leq k < 64} \\{0 \leq n < 128}\end{matrix} \right.} & (25)\end{matrix}$before the method of filtering as in a step S160.

Hence, every loop of the method shown in the flowchart of FIG. 12produces 64 subband samples, each representing the output from onefilter bank subband. As already indicated, in the flowchart of FIG. 12X_(real)[m][l] corresponds to a subband sample l of the QMF subband m,wherein m, l, n are all integers. Hence, the output X_(real)[m][n]equals a real-valued subband sample {circumflex over (x)}_(real,k)^(n,m)({circumflex over (x)}_(real,k) ^(n,m)=X_(real)[m][n]).

While FIG. 12 shows the flowchart of a real-valued analysis QMF bank500, FIG. 13 shows the inventive real to complex converter 520 from FIG.10 in more detail. The real to complex converter 520 shown in FIG. 13receives 64 real subband signals, which form two distinct subsets of Kreal subbands and (64-K) real subbands, wherein K is again a positiveinteger between 1 and 64. The subset of K real subband signals orsubbands forms a plurality of real-valued subband signals, wherein thesecond subset of (64-K) real subbands forms a further plurality ofreal-valued subband signals.

The subset of K real-valued subband signals is provided to both amultiband filter 600 and an optional first delayer 610. The multibandfilter 600 provides at an output a set of K real-valued intermediatesubband signals which are provided to a multiplier 620, which multiplieseach of the real-valued intermediate subband signals with a negativeimaginary unit (−i). An output of the multiplier 620 is provided to anadder 630 which also receives the K real-valued subband signals in adelayed form from the delayer 610. An output of the adder 630 is furtherprovided to a fixed gain adjuster 640. The fixed gain adjuster 640adjusts the level of each subband signal provided at its input bymultiplying the corresponding subband signal with a real-valuedconstant. It should be noted that the fixed gain adjuster 640 is anoptional component, which is not essential for the inventive real tocomplex converter 520. As an output of the fixed gain adjuster 640, ifimplemented, or at the output of the adder 630 the real to complexconverter 520 provides K complex-valued subband signals or rather Kcomplex subbands.

The adder 630 and the multiplier 620 form together a calculator 650,which provides the complex-valued subband signal which can optionally begain adjusted by the fixed gain adjuster 640. To be more precise, thecalculator 650 combines a real-valued subband signal as a real part ofthe complex-valued subband signal output by the calculator 650 and theintermediate signal output by the multiband filter 600 as an imaginarypart of the complex-valued subband signal.

In this context, it is important to note that the first delayer 610 isalso an optional component which ensures that a possible time delaycaused by the multiband filter 600 is correctly taken into accountbefore the calculator 650 combines the intermediate signal output by themultiband filter 600 and the real-valued subband signals provided to thereal to complex converter 520.

As an optional component the real to complex converter 520 alsocomprises a second delayer 660 which also ensures that the possible timedelay caused by the multiband filter 600 does not show up in the (64-K)real-valued subband signals of the further plurality of real-valuedsubband signals. In order to do this, the second delayer 660 isconnected in between the (64-K) real-valued subband signals, which passthe real to complex converter 520 in an unaltered way. It is importantto note that the real to complex converter 520 does not necessarilycomprise any real-valued subband signals being transmitted in anunaltered or only delayed form, as the integer K can also assume thevalue K=64, so that no real-valued subband signal pass the real tocomplex converter 520 in the described way.

Hence, the real QMF subband signals are transformed into partiallycomplex QMF subbands by the real to complex converter 520 as shown inFIG. 13. The first group of K real subband signals is filtered by amultiband filter 600, multiplied by the negative of the imaginary unit(−i) by the multiplier 620 and added to the K delayed real-valuedsubband signals by the adder 630 in order to produce K complex subbandsignals. As already outlined, the delayer 610, which delays the Kreal-valued subband signals before they are processed by the adder 630,is optional. The K complex-valued subband signals output by the adder630 or rather the calculator 650 are gain adjusted by a fixed real gainadjuster 640 and output as the K complex subbands of the real to complexconverter and, hence, of the partially complex analysis filter bank,which comprises the real to complex converter 320.

The second group comprising (64-K) real subband signals are just delayedby the optional second delayer 660, if they exist at all. The role ofboth optional delayers 610, 660 is to compensate for a possible delayintroduced by the multiband filter 600. The length of this delay istypically related to an order of a set of multiband filters comprised inthe multiband filter 600. Typically, the length of this delay is half ofthe order of the multiband prototype filters. This means that the delayimposed by the two optional delayers 610, 660 in the embodiment moreclosely specified below amounts to five subband samples. As already laidout in the sections above, especially with respect to the description ofthe multiband filter in FIG. 4, the multiband filter operates on the Kfirst QMF subband signals by performing the following calculation,wherein {circumflex over (x)}_(imag,k) ^(n,m) represents the output ofthe multiband filter 600 becoming the imaginary part of thecomplex-valued subband signals output by the calculator 650:

$\begin{matrix}{{{\hat{x}}_{{imag},k}^{n,m} = {\sum\limits_{r = {q{(m)}}}^{p{(m)}}{\sum\limits_{v = 0}^{10}{{f_{m,r}\lbrack v\rbrack}{\hat{x}}_{{real},k}^{{n - v},{m + r}}}}}},\mspace{14mu}{m = 0},1,\ldots\mspace{14mu},{K - 1}} & (26)\end{matrix}$

The term f_(m,r)[ν] represents the filters or rather the filterfunctions, {circumflex over (x)}_(real,k) ^(n−ν,m+r) represents thereal-valued subband signals provided at the input of the multibandfilter. Furthermore, the QMF subband summation limits are defined by

$\begin{matrix}{{q(m)} = \begin{Bmatrix}{0,} & {{{for}\mspace{14mu} m} = 0} \\{1,} & {{{{for}\mspace{14mu} m} = 1},\ldots\mspace{14mu},{K - 1}}\end{Bmatrix}} & (27) \\{and} & \; \\{{p(m)} = {\begin{Bmatrix}{1,} & {{{{for}\mspace{14mu} m} = 0},\ldots\mspace{14mu},{K - 2}} \\{0,} & {{{for}\mspace{14mu} m} = {K - 1}}\end{Bmatrix}.}} & (28)\end{matrix}$

The filters f_(m,r)[ν] are derived from two prototype filters of themultiband filter 600, which are mainly determined by two multibandfilter prototype coefficients a^(ν)[n], wherein ν=0,1. To be moreprecise, the filters or rather the filter functions f_(m,r)[ν] fulfilthe relation

$\begin{matrix}{{f_{m,r}\lbrack v\rbrack} = \left\{ \begin{matrix}{{{{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {{- \left( {{2m} + 1} \right)}\left( {v - 5} \right)} \right\rbrack} \right\rbrack}{a^{0}\lbrack v\rbrack}} + {\left( {- 1} \right)^{m}{a^{1}\lbrack v\rbrack}}},\;{{{if}\mspace{14mu}\left( {m,r} \right)} \in \left\{ {\left( {0,0} \right),\left( {{K - 1},0} \right)} \right\}}} \\{{{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {{- r} - {\left( {{2m} + 1 + r} \right)\left( {v - 5} \right)}} \right\rbrack} \right\rbrack}{a^{r}\lbrack v\rbrack}},\;{else}}\end{matrix} \right.} & (29)\end{matrix}$wherein the multiband filter prototype coefficients a⁰[ν] fulfils therelations given in the following Table 1:

0.003 ≦ a⁰[0] ≦ 0.004 | a⁰[1] | ≦ 0.001 −0.072 ≦ a⁰[2] ≦ −0.071 | a⁰[3]| ≦ 0.001 0.567 ≦ a⁰[4] ≦ 0.568 | a⁰[5] | ≦ 0.001 0.567 ≦ a⁰[6] ≦ 0.568| a⁰[7] | ≦ 0.001 −0.072 ≦ a⁰[8] ≦ −0.071 | a⁰[9] | ≦ 0.001 0.003 ≦a⁰[10] ≦ 0.004

Furthermore, the multiband filter prototype coefficients a¹[ν] fulfillthe relations given in the following Table 2:

0.0008 ≦ a¹[0] ≦ 0.0009 0.0096 ≦ a¹[1] ≦ 0.0097 0.0467 ≦ a¹[2] ≦ 0.4680.1208 ≦ a¹[3] ≦ 0.1209 0.2025 ≦ a¹[4] ≦ 0.2026 0.2388 ≦ a¹[5] ≦ 0.23890.2025 ≦ a¹[6] ≦ 0.2026 0.1208 ≦ a¹[7] ≦ 0.1209 0.0467 ≦ a¹[8] ≦ 0.04680.0096 ≦ a¹[9] ≦ 0.0097 0.0008 ≦ a¹[10] ≦ 0.0009

In other words, the filters f_(m,r)[ν] are derived from the prototypefilters as given in Tables 1 and 2 and via Equation 29.

The output {circumflex over (x)}_(imag,k) ^(n,m) of the multiband filter600 is combined by the calculator 650 with a delayed real-valued QMFsubband sample {circumflex over (x)}_(real,k) ^(n−5,m) to form thepartially complex QMF subband samples {circumflex over (x)}_(k) ^(n,m),as illustrated in FIG. 13. To be more precise, the output {circumflexover (x)}_(k) ^(n,m) fulfils the relation

$\begin{matrix}{{\hat{x}}_{k}^{n,m} = \left\{ \begin{matrix}{{\frac{1}{\sqrt{2}}\left( {{\hat{x}}_{{real},k}^{{n - 5},m} - {{\mathbb{i}}\;{\hat{x}}_{{imag},k}^{n,m}}} \right)},} & {{m = 0},1,\ldots\mspace{14mu},{K - 1}} \\{{\hat{x}}_{{real},k}^{{n - 5},m},} & {{m = K},\ldots\mspace{14mu},63}\end{matrix} \right.} & (30)\end{matrix}$wherein in the superscripts (n−5) of the real-valued QMF subband samples{circumflex over (x)}_(real,k) ^(n−5,m) the influence of the twodelayers 610, 660 is illustrated. As mentioned before, the length ofthis delay is typically half of the order of the multiband prototypefilter coefficients a^(ν)[n] as given in Tables 1 and 2. This amounts tofive subband samples.

In a further embodiment of the present invention the multiband filterprototypes or rather multiband filter prototype coefficients a^(ν)[n]with ν=0,1 fulfil the relations given in the following Tables 3 and 4:

TABLE 3 0.00375672984183 ≦ a⁰[0] ≦ 0.00375672984185 | a⁰[1] | ≦0.00000000000010 −0.07159908629243 ≦ a⁰[2] ≦ −0.07159908629241 | a⁰[3] |≦ 0.00000000000010 0.56743883685216 ≦ a⁰[4] ≦ 0.56743883685218 | a⁰[5] |≦ 0.00000000000010 0.56743883685216 ≦ a⁰[6] ≦ 0.56743883685218 | a⁰[7] |≦ 0.00000000000010 −0.07159908629243 ≦ a⁰[8] ≦ −0.07159908629241 | a⁰[9]| ≦ 0.00000000000010 0.00375672984183 ≦ a⁰[10] ≦ 0.00375672984185

TABLE 4 0.00087709635502 ≦ a¹[0] ≦ 0.00087709635504 0.00968961250933 ≦a¹[1] ≦ 0.00968961250935 0.04670597747405 ≦ a¹[2] ≦ 0.046705977474070.12080166385304 ≦ a¹[3] ≦ 0.12080166385306 0.20257613284429 ≦ a¹[4] ≦0.20257613284431 0.23887175675671 ≦ a¹[5] ≦ 0.238871756756730.20257613284429 ≦ a¹[6] ≦ 0.20257613284431 0.12080166385304 ≦ a¹[7] ≦0.12080166385306 0.04670597747405 ≦ a¹[8] ≦ 0.046705977474070.00968961250933 ≦ a¹[9] ≦ 0.00968961250935 0.00087709635502 ≦ a¹[10] ≦0.00087709635504

In a further embodiment of the present invention, the multiband filterprototype coefficients a^(ν)[n] with ν=0,1 comprise the values given inthe following Table 5:

n a⁰[n] a¹[n] 0 0.00375672984184 0.00087709635503 1 0 0.00968961250934 2−0.07159908629242 0.04670597747406 3 0 0.12080166385305 40.56743883685217 0.20257613284430 5 0 0.23887175675672 60.56743883685217 0.20257613284430 7 0 0.12080166385305 8−0.07159908629242 0.04670597747406 9 0 0.00968961250934 100.00375672984184 0.00087709635503

As outlined in the context of the mathematical background, especially inthe context of equations (18) to (20), and the properties of theexpression in equation (18) mentioned above, the resulting structure ofthe coefficients, a^(v)[n] comprise some symmetries. To be more exact,as also the coefficients given in table 5 above show, the coefficientsof a^(v)[n] of table 5 fulfill the symmetry relationsa ^(v)[10−n]=a ^(v) [n]  (30a)for v=0, 1 and n=0, . . . , 10 anda ⁰[2n+1]=0  (30b)for n=0, . . . , 4.

Referring to FIG. 11, prior to the real QMF synthesis 570, the partiallycomplex subband QMF signals are transformed into real-valued QMF signalsby the complex to real converter 560, which is shown in more detail inFIG. 14.

The complex to real converter 560 shown in FIG. 14 receives 64 subbandsignals comprising K complex-valued subband signals and (64-K)real-valued subband signals. A plurality of K complex-valued subbandsignals or other K complex subbands are provided to a fixed gainadjuster 700, which is an optional component of the complex to realconverter 560. As already outlined before, K represents a positiveinteger, which is in the range of 1 to 64. Furthermore, the presentinvention is not limited to 64 subband signals, but can also processmore or less than 64 subband signals. In this case, parameters of theembodiment described below may have to be altered accordingly.

The fixed gain adjuster 700 is connected to a separator 710 or anextractor 710, as explained above, which comprises a real part extractor720 and an imaginary part extractor 730 which both receive the output ofthe fixed gain adjuster 700 as an input. If, however, the optional fixedgain adjuster 700 is not implemented, the separator 710 or extractor 710receives the K complex-valued subband signals directly. The real partextractor 720 is connected to an optional first delayer 740, while theimaginary part extractor 730 is connected to a multiband filter 750.Both, the first delayer 740 and the multiband filter 750 are connectedto a calculator 760 which provides at an output K real-valued subbandsignals as an output of the inventive complex to real converter 560.

Furthermore, the complex to real converter 560 is provided with (64-K)real-valued subband signals, which are also in FIG. 14 referred to asreal subbands, and are provided to a second delayer 770, which is alsoan optional component. At the output of the complex to real converter560 the (64-K) real-valued subband signals are provided in a delayedform. If, however, the second delayer 770 is not implemented, the (64-K)real-valued subband signals are passed on in an unmodified manner.

In the embodiment shown in FIG. 14 the complex part of the partiallycomplex QMF subband signals ŷ_(k) ^(n,m), i.e. the K complex-valuedsubband signals, are gain adjusted by the fixed gain adjuster 700. Thefixed gain adjuster 700 multiplies all incoming complex-valued subbandsignals with the real-valued factor, e.g. 1/√2. Afterwards the separator710 splits the gain adjusted signals into real part signals {circumflexover (μ)}_(k) ^(n,m), and imaginary part signals {circumflex over(ν)}_(k) ^(n,m), by employing the real part extractor 720 and theimaginary part extractor 730 according to

$\begin{matrix}{{{{\hat{u}}_{k}^{n,m} + {{\mathbb{i}}{\hat{v}}_{k}^{n,m}}} = {\frac{1}{\sqrt{2}}{\hat{y}}_{k}^{n,m}}},\mspace{14mu}{m = 0},1,\ldots\mspace{14mu},{K - 1}} & (31)\end{matrix}$

In the embodiment shown in FIG. 14 the factor 1/√2 in front of thecomplex-valued subband signals ŷ_(k) ^(n,m) is provided by the fixedgain adjuster 700.

The multiband filter 750 proceeds to operate on the imaginary partsignals {circumflex over (ν)}_(k) ^(n,m), which are real-valued signals,by performing the following mathematical operation:

$\begin{matrix}{{{\hat{w}}_{k}^{n,m} = {\sum\limits_{r = {q{(m)}}}^{p{(m)}}{\sum\limits_{v = 0}^{10}{{g_{m,r}\lbrack v\rbrack}{\hat{v}}_{k}^{{n - v},{m + r}}}}}},\mspace{14mu}{m = 0},1,\ldots\mspace{14mu},{K - 1}} & (32)\end{matrix}$

The multiband filter 750 provides a set of K real-valued intermediatesubband signals ŵ_(k) ^(m,n). In Equation 32 the QMF subband summationlimits p(m) and q(m) are defined by Equations 27 and 28 of the previoussections, respectively. Furthermore, the filters or rather filterfunctions g_(m,r)[ν] are derived from the prototype filters or ratherthe prototype filter coefficients as laid out in Tables 1 and 2, Tables3 and 4 or in Table 5 via the relation:

$\begin{matrix}{{g_{m,r}\lbrack v\rbrack} = \left\{ \begin{matrix}{{{{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {{- \left( {{2m} + 1} \right)}\left( {v - 5} \right)} \right\rbrack} \right\rbrack}{a^{0}\lbrack v\rbrack}} + {\left( {- 1} \right)^{m}{a^{1}\lbrack v\rbrack}}},\;{{{if}\mspace{14mu}\left( {m,r} \right)} \in \left\{ {\left( {0,0} \right),\left( {{K - 1},0} \right)} \right\}}} \\{{{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {{- r} - {\left( {{2m} + 1 + r} \right)\left( {v - 5} \right)}} \right\rbrack} \right\rbrack}{a^{r}\lbrack v\rbrack}},\;{else}}\end{matrix} \right.} & (33)\end{matrix}$

To obtain the QMF signals ŷ_(real,k) ^(n,m) with respect to the Kcomplex-valued subband signals processed by the separator 710 orextractor 710 and the multiband filter 750, the calculator 760 sumsboth, the intermediate subband signals output by the multiband filter750 and the real part signals output by the separator 710 in the delayedform.

The remaining (64-K) real-valued subband signals are passed on in adelayed form due to the influence of the second delayer 770. Tosummarize, the QMF signals ŷ_(real,k) ^(n,m) to be fed into the real QMFsynthesis bank 570 of FIG. 11 are then obtained by performing theoperation:

$\begin{matrix}{{\hat{y}}_{{real},k}^{n,m} = \left\{ \begin{matrix}{{{\hat{u}}_{k}^{{n - 5},m} + {\hat{w}}_{k}^{n,m}},} & {{m = 0},1,\ldots\mspace{14mu},{K - 1}} \\{{\hat{y}}_{k}^{{n - 5},m},} & {{m = K},\ldots\mspace{14mu},63}\end{matrix} \right.} & (34)\end{matrix}$

As already discussed in context with Equation 30, the superscript (n−5)of both the real part signal û_(k) ^(n−5,m) and the real-valued subbandsignals ŷ_(k) ^(n−5,m) is caused by the first delayer 740 and the seconddelayer 670, wherein typically the length of their delays is once againhalf of the order of the multiband prototype filters a^(ν)[n] as givenin the tables 1 to 5. As explained, this amounts to five subbandsamples.

Also, as explained in context with FIG. 13, the present invention is notlimited to either 64 subband signals or K complex-valued subbandsignals. In fact, the second delayer 770 can also be omitted as thesecond delayer 660 in FIG. 13, if the number of complex-valued subbandsignals K equals the number of all subband signals (K=64). Accordingly,although the number of overall subband signals (integer L=64) is notlimiting or mandatory. By adjusting the appropriate parameters of thecomponents shown in FIG. 14, in principle an arbitrary number of subbandsignals L can be used as an input for the complex to real converter 560.

The present invention is also not limited to multiband filters 204, 306,401, 600, 750 which operate on a symmetric distribution of subbandsignals in relation to the index m over subband. In other words, thepresent invention is not limited to multiband filters, which combinesubband signals or other signals with indices which are symmetricallydistributed with respect to the index of the intermediate subband signaloutput by the multiband filter, e.g. starting from a subband with indexm and an integer m′ by using the subbands with indices m, (m+m′) and(m−m′). Apart from the obvious restriction of subband signals withindices so small or so big that the symmetric choice of subband signalsis out of the questions, the multiband filters can be designed to useindividual combinations of subband signals for each intermediate subbandsignals output by the multiband filter. In other words, also the numberof subband signals processed to obtain the intermediate subband signalscan deviate from three. For instance, if a different filter withdifferent filter coefficients is chosen, as indicated above, it might beadvisable to use more than a total number of three subband signals.Furthermore, the multiband filters can be designed in a way to provideor rather output intermediate subband signals with indices, which do notcorrespond to indices of subband signals provided to the multibandfilter. In other words, if the multiband filter outputs an intermediatesubband signal with an index m, a subband signal having the same indexis not necessarily required as a subband signal provided to themultiband filter.

Additionally, a system comprising one or both converters 520, 560 cancomprise additional aliasing detectors and/or aliasing equalizers orrather aliasing equalization means.

Depending on certain implementation requirements of the inventivemethods, the inventive method can be implemented in hardware or insoftware. The implementation can be performed using a digital storagemedium, in particular a disc, CD or a DVD having electronically readablecontrol signals stored thereon which cooperate with a programmablecomputer system such that the inventive methods are performed.Generally, the present invention is, therefore, a computer programproduct with a program code stored on a machine-readable carrier, theprogram code being operative for performing the inventive method whenthe computer program product runs on a computer. In other words, theinventive methods are, therefore, a computer program having a programcode for performing at least one of the inventive methods when thecomputer program runs on a computer.

While the foregoing has been particularly shown and described withreference to particular embodiments thereof, it will be understood bythose skilled in the art that various other changes in the form anddetails may be made without departing from the spirit and scope thereof.It is to be understood that various changes may be made in adapting todifferent embodiments without departing from the broader conceptdisclosed herein and comprehended by the claims that follow.

1. Apparatus for processing a plurality of real-valued subband signals,the plurality of real-valued subband signals comprising a firstreal-valued subband signal and a second real-valued subband signal, toobtain a complex-valued subband signal, comprising: a multiband filterfor providing a real-valued intermediate subband signal based onfiltering the first real-valued subband signal to obtain a firstfiltered subband signal and the second real-valued subband signal toobtain a second filtered subband signal and based on by combining thefirst filtered subband signal and the second filtered subband signal toobtain the real-valued intermediate subband signal; and a calculator forproviding the complex-valued subband signal by combining the real-valuedsubband signal from the plurality of real-valued subband signals as areal part of the complex-valued subband signal and a signal based on theintermediate subband signal as an imaginary part of the complex-valuedsubband signal, wherein the plurality of real-valued subband signals isoutput by a real QMF analysis bank.
 2. Apparatus according to claim 1,wherein the apparatus comprises a delayer for delaying the real-valuedsubband signal to provide the real-valued subband signal to thecalculator in a delayed form.
 3. Apparatus according to claim 1, whereinthe apparatus comprises a gain adjuster for receiving the complex-valuedsubband signal from the calculator and for adjusting a value of thecomplex-valued subband signal.
 4. Apparatus according to claim 1,wherein a multiband filter is operative to employ a low-pass filtercharacteristics, a high-pass filter characteristics or a bandpass filtercharacteristics for filtering the first real-valued subband signal andfor filtering the second real-valued subband signal.
 5. Apparatusaccording to claim 1, wherein the apparatus is operative to assign toeach real-valued subband signal according to a center frequencyassociated with the real-valued subband signal an index m, so that thereal-valued subband signals are with an increasing index m, arrangedaccording to the center frequency associated with the real-valuedsubband signals, wherein the plurality of real-valued subband signalscomprises K real-valued subband signals, wherein K is a positive integerand m, is an integer in the range from 0 to (K-1).
 6. Apparatusaccording to claim 5, wherein the multiband filter is operative toprovide the real-valued intermediate subband signal with an index m,which corresponds to an index m, associated with the first real-valuedsubband signal.
 7. Apparatus according to claim 6, wherein the multibandfilter is operative to use a real-valued subband signal from theplurality of real-valued subband signals, with which an index (m+1) or(m−1) is associated as the second real-valued subband signal. 8.Apparatus according to claim 6, wherein the multiband filter isoperative to provide a real-valued intermediate subband signal byfurther filtering a third real-valued subband signal to obtain a thirdfiltered subband signal, and by combining the first filtered subbandsignal, the second filtered subband signal and the third filteredsubband signal to obtain the real-valued intermediate subband signal,wherein either an index of the second real-valued subband signal (m−m′)and an index of the third real-valued subband signal is (m+m′) or theindex of the second real-valued subband signal is (m+m′) and the indexof the third real-valued subband signal is (m−m′), wherein m′ is apositive integer, and m is the index of the first real-valued subbandsignal.
 9. Apparatus according to claim 8, wherein the multiband filteris operative to provide a real-valued intermediate subband signal foreach real-valued subband signal as the first real-valued subband signalfrom the plurality of real-valued subband signals with an index m−q(m)from, wherein the index of the second real-valued subband signal is mand the index of the third subband signal is (m+q(m)).
 10. Apparatus(210; 520) according to claim 5, wherein the multiband filter isoperative to provide K intermediate real-valued subband signals having avalue {circumflex over (x)}_(imag, k) ^(n,m), wherein n and m arepositive integers, based on the equation${{\hat{x}}_{{imag},k}^{n,m} = {\sum\limits_{r = {q{(m)}}}^{p{(m)}}{\sum\limits_{v = 0}^{10}{{f_{m,r}\lbrack v\rbrack}{\hat{x}}_{{real},k}^{{n - v},{m + r}}}}}},\mspace{14mu}{m = 0},1,\ldots\mspace{14mu},{K - 1}$for each of the K real-valued subband signals with the index m in therange of 0 to (K- 1) and v is an integer in the range from 0 to 10,wherein ${f_{m,r}\lbrack v\rbrack} = \left\{ \begin{matrix}{{{{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {{- \left( {{2m} + 1} \right)}\left( {v - 5} \right)} \right\rbrack} \right\rbrack}{a^{0}\lbrack v\rbrack}} + {\left( {- 1} \right)^{m}{a^{1}\lbrack v\rbrack}}},{{{if}\mspace{14mu}\left( {m,r} \right)} \in \left\{ {\left( {0,0} \right),\left( {{K - 1},0} \right)} \right\}}} \\{{{\sin\left\lbrack {\frac{\pi}{2}\left\lbrack {{- r} - {\left( {{2m} + 1 + r} \right)\left( {v - 5} \right)}} \right\rbrack} \right\rbrack}{a^{r}\lbrack v\rbrack}},{else}}\end{matrix} \right.$ wherein a⁰[v] and a¹[v] are coefficients of aprototype filter, and wherein each coefficient of the prototype filtera⁰[v] and a¹[v] obey the relations 0.003 ≦ a⁰[0] ≦ 0.004 | a⁰[1] | ≦0.001 −0.072 ≦ a⁰[2] ≦ -0.071 | a⁰[3] | ≦ 0.001 0.567 ≦ a⁰[4] ≦ 0.568 |a⁰[5] | ≦ 0.001 0.567 ≦ a⁰[6] ≦ 0.568 | a⁰[7] | ≦ 0.001 −0.072 ≦ a⁰[8] ≦-0.071 | a⁰[9] | ≦ 0.001 0.003 ≦ a⁰[10] ≦ 0.004

and 0.0008 ≦ a¹[0] ≦ 0.0009 0.0096 ≦ a¹[1] ≦ 0.0097 0.0467 ≦ a¹[2] ≦0.0468 0.1208 ≦ a¹[3] ≦ 0.1209 0.2025 ≦ a¹[4] ≦ 0.2026 0.2388 ≦ a¹[5] ≦0.2389 0.2025 ≦ a¹[6] ≦ 0.2026 0.1208 ≦ a¹[7] ≦ 0.1209 0.0467 ≦ a¹[8] ≦0.0468 0.0096 ≦ a¹[9] ≦ 0.0097 0.0008 ≦ a¹[10] ≦ 0.0009.


11. Apparatus (210; 520) according to claim 10, wherein the multibandfilter is designed so that the coefficients of the prototype filtersa⁰[v] and a^(l) [v] obey the relations 0.00375672984183 ≦ a⁰[0] ≦0.00375672984185 | a⁰[1] | ≦ 0.00000000000010 −0.07159908629243 ≦ a⁰[2]≦ -0.07159908629241 | a⁰[3] | ≦ 0.00000000000010 0.56743883685216 ≦a⁰[4] ≦ 0.56743883685218 | a⁰[5] | ≦ 0.00000000000010 0.56743883685216 ≦a⁰[6] ≦ 0.56743883685218 | a⁰[7] | ≦ 0.00000000000010 −0.07159908629243≦ a⁰[8] ≦ -0.07159908629241 | a⁰[9] | ≦ 0.000000000000100.00375672984183 ≦ a⁰[10] ≦ 0.00375672984185

and 0.00087709635502 ≦ a¹[0] ≦ 0.00087709635504 0.00968961250933 ≦ a¹[1]≦ 0.00968961250935 0.04670597747405 ≦ a¹[2] ≦ 0.046705977474070.12080166385304 ≦ a¹[3] ≦ 0.12080166385306 0.20257613284429 ≦ a¹[4] ≦0.20257613284431 0.23887175675671 ≦ a¹[5] ≦ 0.238871756756730.20257613284429 ≦ a¹[6] ≦ 0.20257613284431 0.12080166385304 ≦ a¹[7] ≦0.12080166385306 0.04670597747405 ≦ a¹[8] ≦ 0.046705977474070.00968961250933 ≦ a¹[9] ≦ 0.00968961250935 0.00087709635502 ≦ a¹[10] ≦0.00087709635504.


12. Apparatus according to claim 5, wherein the calculator is operativeto provide K complex-valued subband signals with an index m and a value{circumflex over (x)}_(imag, k) ^(n, m) , wherein k, n, m are integers,wherein m is in the range from 0 to (K-1), based on the equation${{\hat{x}}_{k}^{n,m} = {\frac{1}{\sqrt{2}}\left( {{\hat{x}}_{{real},k}^{{n - 5},m} - {{\mathbb{i}}\;{\hat{x}}_{{imag},k}^{n,m}}} \right)}},\mspace{14mu}{m = 0},1,\ldots\mspace{14mu},{K - 1}$wherein {circumflex over (x)}_(real, k) ^(n, m) represents a value of areal-valued subband signal and {circumflex over (x)}_(imag, k) ^(n, m)represents a value of a real-valued intermediate subband signal and irepresents the complex unit according toi=√{square root over (−1)}.
 13. Apparatus according to claim 5, whereinthe apparatus is operative to receive a further plurality of real-valuedsubband signals comprising (L-K) real-valued subband signals and toprovide the further plurality of real-valued subband signals asreal-valued subband signals, wherein L is a positive integer and whereinL is greater or equal to K.
 14. Apparatus (210; 520) according to claim13, wherein the apparatus is designed so that the positive integer Lequals
 64. 15. Apparatus according to claim 13, wherein the apparatuscomprises a further delayer for delaying the real-valued subband signalsof the further plurality of real-valued subband signals and wherein theapparatus is operative to provide the further plurality of real-valuedband signals in a delayed form.
 16. System comprising: an analysisfilter bank for processing an audio input signal into a plurality ofreal-valued subband signals; an apparatus for processing the pluralityof real-valued subband signals to obtain a complex-valued subband signalaccording to claims 1; a modifier for receiving the complex-valuedsubband signal and for providing the complex-valued subband signal in amodified form; an apparatus to obtain a real-valued subband signal; anda synthesis filter bank for processing the real-valued subband signalinto an audio output signal.
 17. System according to claim 16, whereinthe analysis filterbank is designed such that the plurality ofreal-valued subband signals comprises L real-valued subband signals,wherein L is a positive integer, wherein the apparatus for processingthe plurality of real-valued subband signals is designed such that theapparatus provides a plurality of complex-valued subband signals and afurther plurality of real-valued subband signals; wherein the pluralityof complex-valued subband signals comprises K complex-valued subbandsignals and the further plurality of real-valued subband signalscomprise (L-K) real-valued subband signals; wherein K is an integer inthe range from 1 to L; wherein the modifier is operative to modify the Kcomplex-valued subband signals of the plurality of complex-valuedsubband signals to provide K complex-valued subband signals in amodified form; wherein the system further comprises a further modifierfor modifying the further plurality of real-valued subband signals andfor providing the further plurality of real-valued subband signals in amodified form; wherein the apparatus is designed to process theplurality of complex-valued subband signals comprising K real-valuedsubband signals and the further plurality of real-valued subband signalscomprising (L-K) real-valued subband signals to obtain a final pluralityof real-valued subband signals, wherein the final plurality ofreal-valued subband signals comprises L real-valued subband signals; andwherein the synthesis filter band is designed such that the finalplurality of real-valued subband signals is processed into the audiooutput signal.
 18. Method for processing a plurality of real-valuedsubband signals, the plurality of real-valued subband signals comprisinga first real-valued subband signal and a second real-valued subbandsignal to obtain a complex-valued subband signal, comprising: filtering,by a multiband filter, the first real-valued subband signal to obtain afirst filtered subband signal and the second real-valued subband signalto obtain a second filtered subband signal; combining the first filteredsubband signal and the second filtered subband signal when deriving areal-valued intermediate subband signal; and combining, by a calculator,a real-valued subband signal from the plurality of real-valued subbandsignals as a real part of a complex-valued subband signal and a signalwhich is based on the intermediate subband signal as an imaginary partof the complex-valued subband signal, wherein the plurality ofreal-valued subband signals is output by a real QMF analysis bank. 19.Non-transitory storage medium having stored thereon a computer programfor performing, when running on a computer, a method in accordance withthe method of claim 18.